Root clustering of words

Lischke, Gerhard. "Root clustering of words." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 48.3 (2014): 267-280. <http://eudml.org/doc/273086>.

@article{Lischke2014,
abstract = {Six kinds of both of primitivity and periodicity of words, introduced by Ito and Lischke [M. Ito and G. Lischke, Math. Log. Quart. 53 (2007) 91–106; Corrigendum in Math. Log. Quart. 53 (2007) 642–643], give rise to defining six kinds of roots of a nonempty word. For 1 ≤ k ≤ 6, a k-root word is a word which has exactly k different roots, and a k-cluster is a set of k-root words u where the roots of u fulfil a given prefix relationship. We show that out of the 89 different clusters that can be considered at all, in fact only 30 exist, and we give their quasi-lexicographically smallest elements. Also we give a sufficient condition for words to belong to the only existing 6-cluster. These words are also called Lohmann words. Further we show that, with the exception of a single cluster, each of the existing clusters contains either only periodic words, or only primitive words.},
author = {Lischke, Gerhard},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {periodicity of words; primitivity of words; roots of words; classification of words},
language = {eng},
number = {3},
pages = {267-280},
publisher = {EDP-Sciences},
title = {Root clustering of words},
url = {http://eudml.org/doc/273086},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Lischke, Gerhard
TI - Root clustering of words
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 3
SP - 267
EP - 280
AB - Six kinds of both of primitivity and periodicity of words, introduced by Ito and Lischke [M. Ito and G. Lischke, Math. Log. Quart. 53 (2007) 91–106; Corrigendum in Math. Log. Quart. 53 (2007) 642–643], give rise to defining six kinds of roots of a nonempty word. For 1 ≤ k ≤ 6, a k-root word is a word which has exactly k different roots, and a k-cluster is a set of k-root words u where the roots of u fulfil a given prefix relationship. We show that out of the 89 different clusters that can be considered at all, in fact only 30 exist, and we give their quasi-lexicographically smallest elements. Also we give a sufficient condition for words to belong to the only existing 6-cluster. These words are also called Lohmann words. Further we show that, with the exception of a single cluster, each of the existing clusters contains either only periodic words, or only primitive words.
LA - eng
KW - periodicity of words; primitivity of words; roots of words; classification of words
UR - http://eudml.org/doc/273086
ER -